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Henry S

(7,3,2) triangle tiling (small)

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(7,3,2) triangle tiling (small) by henryseg full viewable 3d model
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0 Likes1 DownloadsFebruary 28, 2022

This model is restricted by licensing terms. 

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This model is restricted by licensing terms. 

0 Likes1 DownloadsFebruary 28, 2022

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Model originally uploaded to Thingiverse at https://www.thingiverse.com/thing:477006. A [larger version](http://www.thingiverse.com/thing:1608550) of this model is featured in figures 4.13 and 4.14 of [Visualizing Mathematics with 3D Printing](http://3dprintmath.com). This 3D printed illustration of the hyperbolic plane is joint work with Saul Schleimer. The hyperbolic plane has constant negative curvature - it is shaped like a saddle everywhere. The hyperbolic plane cannot be "seen" directly. This is similar to the problem faced by terrestrial mapmakers: any flat map of the earth necessarily distorts either size or distance. This 3D print is a model, called the hemisphere model, of the hyperbolic plane. Lighting the piece, in three different ways, casts shadows of three further models: the Poincaré disk model (first image), the Klein model (second image) and the upper half space (third and fourth images) model. Each triangle in the (7,3,2) tiling has angles pi/2, pi/3 and pi/7. This is very unlike triangles in Euclidean geometry, where the angles must add to pi. In fact, all of the triangles in our illustration are identical! Some look smaller than others, but this is an artifact of the promised, and unavoidable, distortion. [This model](http://shpws.me/w1Mz), and the [larger, more detailed version](http://shpws.me/w1LW) are also available from Shapeways.




0 Likes1 DownloadsFebruary 28, 2022

This model is restricted by licensing terms. 

Community Uploads

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This model is restricted by licensing terms. 

0 Likes1 DownloadsFebruary 28, 2022

Community Uploads

No photos added yet, be the first to upload a photo!